The (D) Property in Banach Spaces

Danyal Soybaş

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: A Banach space E is said to have (D) property if every bounded linear operator T : F → E* is weakly compact for every Banach space F whose dual does not contain an isomorphic copy of l∞. Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space L1(v) of real functions, which are integrable with respect to a measure v with values in a Banach space X, has (D) property. We give some other results concerning Banach spaces with (D) property.

Date: 2012
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https://doi.org/10.1155/2012/754531

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:754531

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